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  1. Shaughan Lavine (2006). Something About Everything: Universal Quantification in the Universal Sense of Universal Quantification. In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. 98--148.
     
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  2. Shaughan Lavine (2005). 2005 Spring Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 11 (4):547-556.
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  3. Scot Adams, Shaughan Lavine, Zlil Sela, Natarajan Shankar, Stephen Simpson, Stevo Todorcevic & Theodore A. Slaman (2003). University of Nevada, Las Vegas, Las Vegas, Nevada June 1–4, 2002. Bulletin of Symbolic Logic 9 (1).
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  4. Shaughan Lavine (2000). Quantification and Ontology. Synthese 124 (1-2):1-43.
    Quineans have taken the basic expression of ontological commitment to be an assertion of the form '' x '', assimilated to theEnglish ''there is something that is a ''. Here I take the existential quantifier to be introduced, not as an abbreviation for an expression of English, but via Tarskian semantics. I argue, contrary to the standard view, that Tarskian semantics in fact suggests a quite different picture: one in which quantification is of a substitutional type apparently first proposed by (...)
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  5. Ruth Barcan Marcus & Shaughan Lavine (1995). Modalities: Philosophical Essays. British Journal for the Philosophy of Science 46 (2):267-274.
     
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  6. Shaughan Lavine (1995). Finite Mathematics. Synthese 103 (3):389 - 420.
    A system of finite mathematics is proposed that has all of the power of classical mathematics. I believe that finite mathematics is not committed to any form of infinity, actual or potential, either within its theories or in the metalanguage employed to specify them. I show in detail that its commitments to the infinite are no stronger than those of primitive recursive arithmetic. The finite mathematics of sets is comprehensible and usable on its own terms, without appeal to any form (...)
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  7. Shaughan Lavine (1995). Review. [REVIEW] British Journal for the Philosophy of Science 46 (2):267-274.
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  8. Shaughan Lavine (1994). Understanding the Infinite. Harvard University Press.
    An engaging account of the origins of the modern mathematical theory of the infinite, his book is also a spirited defense against the attacks and misconceptions ...
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  9. Shaughan Lavine (1993). Generalized Reduction Theorems for Model-Theoretic Analogs of the Class of Coanalytic Sets. Journal of Symbolic Logic 58 (1):81-98.
    Let A be an admissible set. A sentence of the form ∀R̄φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence if φ ∈ A (φ is $\bigvee\Phi$ , where Φ is an A-r.e. set of sentences from A; φ ∈ Lω1ω). A sentence of the form ∃R̄φ is an ∃2(A) (∃s 2(A),∃2(Lω1ω)) sentence if φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence. A class of structures is, for example, a ∀1(A) class if it is the class of models of a ∀1(A) sentence. Thus (...)
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  10. Gerald Feinberg, Shaughan Lavine & David Albert (1992). Knowledge of the Past and Future. Journal of Philosophy 89 (12):607-642.
  11. Shaughan Lavine (1992). A Spector-Gandy Theorem for cPCd(A) Classes. Journal of Symbolic Logic 57 (2):478 - 500.
    Let U be an admissible structure. A cPCd(U) class is the class of all models of a sentence of the form $\neg\exists\bar{K} \bigwedge \Phi$ , where K̄ is an U-r.e. set of relation symbols and φ is an U-r.e. set of formulas of L∞ω that are in U. The main theorem is a generalization of the following: Let U be a pure countable resolvable admissible structure such that U is not Σ-elementarily embedded in HYP(U). Then a class K of countable (...)
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  12. Shaughan Lavine (1992). A Spector-Gandy Theorem for $Mathrm{cPC}_d(Mathbb{A})$ Classes. Journal of Symbolic Logic 57 (2):478-500.
    Let $\mathfrak{U}$ be an admissible structure. A $\mathrm{cPC}_d(\mathfrak{U})$ class is the class of all models of a sentence of the form $\neg\exists\bar{K} \bigwedge \Phi$, where $\bar{K}$ is an $\mathfrak{U}$-r.e. set of relation symbols and $\phi$ is an $\mathfrak{U}$-r.e. set of formulas of $\mathscr{L}_{\infty\omega}$ that are in $\mathfrak{U}$. The main theorem is a generalization of the following: Let $\mathfrak{U}$ be a pure countable resolvable admissible structure such that $\mathfrak{U}$ is not $\Sigma$-elementarily embedded in $\mathrm{HYP}(\mathfrak{U})$. Then a class $\mathbf{K}$ of countable structures (...)
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  13. Shaughan Lavine (1992). Review of Maddy, Realism in Mathematics. [REVIEW] Journal of Philosophy 89 (6):321-326.
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  14. Shaughan Lavine (1991). Dual Easy Uniformization and Model-Theoretic Descriptive Set Theory. Journal of Symbolic Logic 56 (4):1290-1316.
    It is well known that, in the terminology of Moschovakis, Descriptive set theory (1980), every adequate normed pointclass closed under ∀ω has an effective version of the generalized reduction property (GRP) called the easy uniformization property (EUP). We prove a dual result: every adequate normed pointclass closed under ∃ω has the EUP. Moschovakis was concerned with the descriptive set theory of subsets of Polish topological spaces. We set up a general framework for parts of descriptive set theory and prove results (...)
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  15. Shaughan Lavine (1991). Is Quantum Mechanics an Atomistic Theory? Synthese 89 (2):253 - 271.
    If quantum mechanics (QM) is to be taken as an atomistic theory with the elementary particles as atoms (an ATEP), then the elementary particlcs must be individuals. There must then be, for each elementary particle a, a property being identical with a that a alone has. But according to QM, elementary particles of the same kind share all physical properties. Thus, if QM is an ATEP, identity is a metaphysical but not a physical property. That has unpalatable consequences. Dropping the (...)
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